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Mat. Zametki, 1972, Volume 12, Issue 2, Pages 197–204 (Mi mz9868)  

This article is cited in 9 scientific papers (total in 9 papers)

Graded algebras

V. E. Govorov

Moscow Institute of Electronic Machinery

Abstract: We study the growth in the number of dimensions $d_n$ of the homogeneous component of a graded algebra with a finite number of defining relations and generators for the Poincaré series $\sum d_nx^n$. It is proved that if the defining relations are words, the Poincaré series is a rational function. In the general case inequalities are proved linking the number of dimensions $d_n$ with the number of generators defining relations and their degree.

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English version:
Mathematical Notes, 1972, 12:2, 552–556

Bibliographic databases:

UDC: 519.4
Received: 05.04.1971

Citation: V. E. Govorov, “Graded algebras”, Mat. Zametki, 12:2 (1972), 197–204; Math. Notes, 12:2 (1972), 552–556

Citation in format AMSBIB
\Bibitem{Gov72}
\by V.~E.~Govorov
\paper Graded algebras
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 2
\pages 197--204
\mathnet{http://mi.mathnet.ru/mz9868}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=318199}
\zmath{https://zbmath.org/?q=an:0239.16002}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 2
\pages 552--556
\crossref{https://doi.org/10.1007/BF01095017}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. I. Grigorchuk, “Degrees of growth of finitely generated groups, and the theory of invariant means”, Math. USSR-Izv., 25:2 (1985), 259–300  mathnet  crossref  mathscinet  zmath
    2. V. E. Govorov, “Codes and homology”, Math. USSR-Sb., 52:1 (1985), 275–282  mathnet  crossref  mathscinet  zmath
    3. I. K. Babenko, “Problems of growth and rationality in algebra and topology”, Russian Math. Surveys, 41:2 (1986), 117–175  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. A. Ufnarovskii, “On the use of graphs for computing a basis, growth and Hilbert series of associative algebras”, Math. USSR-Sb., 68:2 (1991), 417–428  mathnet  crossref  mathscinet  zmath  isi
    5. D. I. Piontkovskii, “Hilbert series and their relations in algebras”, Russian Math. Surveys, 53:6 (1998), 1360–1361  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. D. I. Piontkovskii, “Hilbert series and relations in algebras”, Izv. Math., 64:6 (2000), 1297–1311  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. D. I. Piontkovskii, “On graded algebras of global dimension 3”, Izv. Math., 65:3 (2001), 557–568  mathnet  crossref  crossref  mathscinet  zmath  elib
    8. A. M. Shur, “O vychislenii parametrov i tipov povedeniya kombinatornoi slozhnosti regulyarnykh yazykov”, Tr. IMM UrO RAN, 16, no. 2, 2010, 270–287  mathnet  elib
    9. Dilber Koçak, “Finitely presented quadratic algebras of intermediate growth”, Algebra Discrete Math., 20:1 (2015), 69–88  mathnet  mathscinet
  • Математические заметки Mathematical Notes
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